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Modeling the Kinetics of Enzymic Reactions in Mainlyh Solid Reaction Mixtures

机译：模拟主要固体反应混合物中酶反应的动力学

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摘要

There is currently considerable interest in using mainly solid reaction mixtures for enzymic catalysis. In these reactions starting materials dissolve into, and product materials crystalize out of, a small amount of liquid phase in which the catalytic reaction occurs. An initial mathematical model for mass transfer effects in such systems is constructed using some physically reasonable approximations. The model equations are solved numerically to determine how the reactant concentrations very with time and position. To evaluate the extent to which mass transfer limits the overall rate of product formation, an effectiveness factor is defined as the ratio of the observed total reaction rate to the total reaction rate in the reaction limited limit. As expected, the value of the effectiveness factor in steady state is strongly dependent on the Thiele modulus. However, it is also observed that the effectiveness factor can vary widely as a result of changes in the other dimensionless groups characterizing the system. For example, there are situations with Thiele modulus equal to unity in which the value of the effectiveness factor varies between approximately 0.1 and 0.8 as the other parameters are varied in physically reasonable ranges. Analytical asymptotic solutions that provide good approximations to the numerically calculated results in various physically important limiting cases are also presented.
机译：当前，主要使用固体反应混合物进行酶催化引起了极大的兴趣。在这些反应中，原料溶解在少量发生催化反应的液相中，而产物物质从其中结晶出来。使用某些物理上合理的近似值，可以构建此类系统中传质效应的初始数学模型。对模型方程进行数值求解，以确定反应物如何随时间和位置而非常集中。为了评估传质限制产物形成总速率的程度，将有效因子定义为观察到的总反应速率与反应极限范围内总反应速率之比。不出所料，稳定状态下的有效系数值在很大程度上取决于Thiele模量。但是，还可以观察到，由于表征该系统的其他无量纲基团的变化，效果因子的变化范围可能很大。例如，在Thiele模量等于1的情况下，当其他参数在物理上合理的范围内变化时，有效系数的值将在0.1到0.8之间变化。还提出了在各种物理上重要的极限情况下可以很好地逼近数值计算结果的解析渐近解。

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